Tunneling reactions, rate constants

Figure 22. Thermal reaction rate constant of Hj. Solid line-without tunneling. Dotted hne-with tunneling. Taken from Ref. [9].

Using eqns. (42)-(44) and assuming T > co /2n, i.e. that the temperature is not too low, we have that tunneling does not practicably influence the macroscopic reaction rate constant at high pressures when the molecules have an equilibrium energy distribution. In this case... 

Thus, expression (59) enables us to describe the solid-state reaction rate constant dependence on the parameters of the potential barrier and medium properties in a wide temperature range, from liquid helium temperatures when the reaction runs by a tunneling mechanism to high temperatures (naturally, not exceeding the melting point) when the transition is of the activation type. 

The need to include quantum mechanical effects in reaction rate constants was realized early in the development of rate theories. Wigner [8] considered the lowest order terms in an -expansion of the phase-space probability distribution function around the saddle point, resulting in a separable approximation, in which bound modes are quantized and a correction is included for quantum motion along the reaction coordinate - the so-called Wigner tunneling correction. This separable approximation was adopted in the standard ad hoc procedure for quan-... 

For reactions involving light atoms, particularly hydrogen atom or proton transfer reactions, a major correction to the reaction rate constant is due to tunneling [11, 12, 58, 64, 76, 96, 106, 111, 112, 114-116, 129, 132, 133, 143-152]. 

Table 4 Logarithm of the reaction rate constant, log(A /[cm mol s ]), as a function of temperature, for the reactions CH4 + CH CH + CH4 (reaction 1) and CH4 + CH — H - - C2H6 (reaction 2). The transmission coefficient k accounting for tunneling effects is also given.

Disregarding the tunnel effects (see Sect. 1.5) and staying within the approximation rigid rotator-harmonic oscillator, one may, for the biomolecular reaction A -h B), calculate the kinetic isotopic effect (ratio between the reaction rate constant of the compound with the light isotope and the rate constant K2 of the compound containing the heavy isotope) from the Bigeleisen equation ... 

One fundamental assumption in classical transition state theory is that of no recrossing over the transition state. The advantage, of the RP theory is therefore that since it provides a hamiltonian it can be used in dynamical calculations thereby incorporating the effect of recrossing. However, it is also possible to use the hamiltonian for an estimate of the transmission factor, i.e. the correction to transition state theory from recrossing of the trajectories. An additional correction factor comes from quantum tunneling (see below). Considering the reaction rate constant it may be expressed as... 

Thebook reviews low-dimensional theories and clarifies their insufficiency conceptually and numerically. It also examines the phenomenon of nonadiabatic tunneling, which is common in molecular systems. The book describes applications to real polyatomic molecules, such as vinyl radicals and malonaldehyde, demonstrating the high efficiency and accuracy of the method. It discusses tunneling in chemical reactions, including theories for direct evaluation of reaction rate constants for both electronically adiabatic and nonadiabatic chemical reactions. In the final chapter, the authors touch on future perspectives. 

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